Control of Nonlocal Magnon Spin Transport via Magnon Drift Currents

Spin transport via magnon diffusion in magnetic insulators is important for a broad range of spin-based phenomena and devices. However, the absence of the magnon equivalent of an electric force is a bottleneck. In this Letter, we demonstrate the controlled generation of magnon drift currents in heterostructures of yttrium iron garnet and platinum. By performing electrical injection and detection of incoherent magnons, we find magnon drift currents that stem from the interfacial Dzyaloshinskii-Moriya interaction. We can further control the magnon drift by the orientation of the magnetic field. The drift current changes the magnon propagation length by up to $\pm 6\%$ relative to diffusion. We generalize the magnonic spin transport theory to include a finite drift velocity resulting from any inversion asymmetric interaction and obtain results consistent with our experiments.

Figure 1

(a) Driving an electrical current $I$ in the central wire generates a spin accumulation (open dashed arrows) via the spin Hall effect so that magnons can be excited in the YIG layer. In the presence of DMI, a finite drift velocity ${\mathbf{v}}_{\mathrm{DMI}}$ (blue arrows) is superposed onto the random diffusive magnon motion (orange arrows). Thus, the higher number of magnons propagating to the left Pt wire compared to the right one leads to a difference in magnon population and in turn a different inverse spin Hall current $I_{\mathrm{nl}}$. (b) The magnon dispersion relation in a system with finite DMI (red line) has a symmetric parabolic dispersion (gray dashed line), which leads to random diffusion and an asymmetric (linear) contribution due to DMI (blue dash-dotted line) that results in unidirectional drift. (c) For interfacial DMI, the orientation of the drift velocity is orthogonal to the in-plane magnetization, providing control over the drift velocity along the magnon propagation direction $\widehat{\mathbf{y}}$ [see Eq. (1)]. (d) Optical micrograph of a representative three wire device and sketches of the electrical wiring and coordinate system.

Figure 2

(a) The nonlocal resistance $R_{1\omega }$ of the left (black line) and right (orange line) wire shows a different dependence on magnetic field orientation $\alpha$. $R_{1\omega ,\mathrm{R}}$ has been rescaled by 0.4% to scale with $R_{1\omega ,\mathrm{L}}$, a difference arising from device imperfections. Additionally, a constant offset arising from inductive or capacitive coupling has been removed from both curves [8]. (b) The difference between the two curves in panel (a) (gray circles) corresponds to a difference in magnons transported to the left and right Pt wire. The blue curve represents a $A_{1\omega }{\sin }^2(\alpha )\cos (\alpha )$ angular dependence. The shaded blue (red) regions correspond to enhanced (reduced) magnon transport toward the left wire. (c) The average of the two curves in panel (a) (solid gray squares). The thickness of the YIG film is $t_{\mathrm{YIG}}=50\mathrm{nm}$. The red curve represents a $S_{1\omega }{\sin }^2(\alpha )$ dependence, which is expected in the absence of a drift contribution.

Figure 3

(a) Dependence of $\mathrm{\Delta }{R}_{1\omega }$ and (b) $\mathrm{\Sigma }{R}_{1\omega }$ on the wire separation $d_{\mathrm{nl}}$. The gray (orange) symbols correspond to $d_{\mathrm{nl}}=1.5\mu \mathrm{m}$ ($2.0\mu \mathrm{m}$), and the solid lines are fits of the respective angular dependencies. (c) $A_{1\omega }/S_{1\omega }$ increases linearly with the distance $d_{\mathrm{nl}}$ between the central wire and the wires to the left and right (red line). The error bars are estimated from fits to the angular dependency of $\mathrm{\Delta }{R}_{1\omega }$ and $\mathrm{\Sigma }{R}_{1\omega }$. (d) The normalized directional propagation length as a function of the inverse of $t_{\mathrm{YIG}}$. The error for $\delta \lambda /{\lambda }_0$ is evaluated from the fits to the distance dependence of $A_{1\omega }/S_{1\omega }$ and $S_{1\omega }$ and the shaded red area corresponds to the error of the linear fit.